Statistician Crunches the Numbers for an Algorithm of Broadway Hits

Any Broadwayproducer will tell you there’s no magic formula for Broadway success. But that doesn’t stop some people from trying to find one.

Particularly statisticians. Suspecting there’s a golden ratio that might help explain “The Phantom of the Opera,” “The Lion King” or “Wicked,” mathematician Marc Hershberg gave it a go, crunching the numbers as part of his graduate studies in the Department of Organizational Behavior at Cornell University’s School of Industrial and Labor Relations.

The result: A multi-variable linear regression model (you know, one of those) that purportedly predicts the lifespan of a Broadway show.

Prior investigations into the science of Broadway hits have included a 2012 study that found, among other things, that shows that won Tonys in certain major categories could add 50% on to their life expectancy. A 2004 paper similarly inspected the statistical properties of hits and flops. Data for those two studies, however, incorporated limited engagements — like the 16-weeks-and-done runs of star-driven plays, which are only on the boards a short time regardless of B.O. success. Herschberg bet that if he eliminated those predetermined lifespans, he could come up with a more accurate statistical model.

The fact that the study draws its data only from shows that ran on Broadway between 1988 and 2003 — time and manpower constraints kept Herschberg from going further, he said — may raise a few skeptical eyebrows among theater industry types, and the report’s takeaways tend to confirm conventional wisdom such as the fact that spectacle musicals with larger casts are most likely to run longer.

Still, it’s Herschberg’s linear regression model that could turn a few heads. He narrowed down 14 intrinsic characteristics, including cast size and whether a show is a musical or a revival, and came up with a formula that calculates a production’s projected lifespan. Then he tried it out on a random sampling of 10 shows, and the accuracy was impressive.

According to the model, the 2000 musical “James Joyce’s The Dead” should have run 110 performances; it ran 112. The 1990 revival of “Fiddler on the Roof” had an expected run of 239 shows and an actual run of 241. The 1999 play “Epic Proportions” played 92 perfs — exactly the number of shows predicated by the formula. In fact, the expected lifespan for each of the ten test cases fell within seven performances of its actual finish.

Nothing’s an exact science on Broadway, of course. But Herschberg said he hopes his formula could offer career guidance to producers or auditioning actors, steering them toward projects that have a better chance of success.